Fractal Sets as Final Coalgebras Obtained by Completing an Initial Algebra

This paper is a contribution to the presentation of fractal sets in terms of final coalgebras.The first result on this topic was Freyd's Theorem: the unit interval [0,1] is the final coalgebra ofa certain functor on the category of bipointed sets. Leinster 2011 offersa sweeping generalization of this result. He is able to represent many of what would be intuitivelycalled "self-similar" spaces using (a) bimodules (also called profunctors or distributors),(b) an examination of non-degeneracy conditions on functors of various sorts; (c) a construction offinal coalgebras for the types of functors of interest using a notion of resolution. In addition to thecharacterization of fractals sets as sets, his seminal paper also characterizes them as topological spaces.Our major contribution is to suggest that in many cases of interest, point (c) above on resolutionsis not needed in the construction of final coalgebras. Instead, one may obtain a number of spaces ofinterest as the Cauchy completion of an initial algebra,and this initial algebra is the set of points in a colimit of an omega-sequence of finite metric spaces.This generalizes Hutchinson's 1981 characterization of fractal attractors asclosures of the orbits of the critical points. In addition to simplifying the overall machinery, it also presents a metric space which is ``computationally related'' to the overall fractal. For example, when applied to Freyd's construction, our method yields the metric space.of dyadic rational numbers in [0,1].Our second contribution is not completed at this time, but it is a set of results on \emph{metric space}characterizations of final coalgebras. This point was raised as an open issue in Hasuo, Jacobs, and Niqui 2010,and our interest in quotient metrics comes from their paper. So in terms of (a)--(c) above, our workdevelops (a) and (b) in metric settings while dropping (c).

FEMALE IDENTITY AND MAGICAL REALISM IN NATIVE AMERICAN AND AFRO AMERICAN WOMEN WRITING: A COMPARATIVE ANALYSIS OF LOUISE ERDRICH’S TRACKS AND TONY MORRISON’S BELOVED

<p>This research article is an attempt to evaluate the Native and Afro American women writers ‘sustained efforts to articulate a continuous and internal cultural female identity by constructing re evaluative narratives that deconstruct institutionally supported universal female images inflicted upon the third and fourth world women by the first world feminist intelligentsia. To do so these women writers radically depart from the conventions of Euro American stylistic, formal and structural modalities of the narrative and use instead a stylistic mosaic allowing the native and black oral traditions to imbricate with the white normative models. Since literature and arts have always been an effective medium, an expansive domain, and a discursive field where writers have been voicing the aureate human feelings, conflicting passions and the continuous struggles of the different societal segments, especially of deprived strata against those who maintain and perpetuate their cultural and political hegemony by suppressing the subalterns, the women writers from the fourth world ethnic communities have expressed whole range of the intensely personal and communal human emotions that radiate from the springboard of social, cultural, historic and political practices One of the significant features that the Native American and Afro American women writers often demonstrate include the use of magical realist strategies that express, on one hand, their efforts to indigenize narrative and, on the other hand, help them construct female identity from their own perspective since, within main concerns of contemporary fourth world feminist criticism, the (re) construction of female identity merits special attention and analysis. The stereotypical discursive construction of the Native and Afro American women by the dominant Euro American discourses bracketed them into essentialist categories glossing over the medley of vital differences that these women reveal in their social, cultural, anthropological and sexual strictures. Tackling the issue of the discursive construction of female identity that involves conceptual and perspectival problems, both Native American and Afro American women writers deconstruct the sweeping generalization of the fourth world women by challenging and subverting the clichéd images replacing them with empowered and agentive subjects who are no more subjected to, what Gyatri Spivk conceptualizes, subalternity and “epistemic violence”.</p>

The Tourism of Titillation in Tijuana and Niagara Falls: Cross-Border Tourism and Hollywood Films between 1896 and 1960

In the popular imaginary, Tijuana, Mexico is notorious for its liberal laws concerning prostitution, gambling, and narcotics. Conversely, Niagara Falls, Canada apparently offers visitors only wholesome attractions. Yet this sweeping generalization belies the historic parallels that exist between these iconic border towns. In Hollywood films, both Tijuana and Niagara Falls figure as liminal locations of crossing and collision, as well as permissive zones defined by sex, tourism, and consumption. This essay explores the intertwined cultural arenas of film and tourism by analyzing cinematic representations of Tijuana and Niagara Falls as cross-border tourist destinations. By examining how cinematic representations of these urbanized border regions have changed over time, I demonstrate how Hollywood, as a hegemonic culture industry, responded to the United States’ evolving relationships with its northern and southern neighbors. This study offers a hemispheric and comparative approach to the study of urban borders, tourism, and visual culture.

Victims of attempted murder in India: An analysis of impact of victimization and responses of criminal justice system

The problem of murder is not new phenomenon in India. Today large number of murders, attempt to murder are occurring for financial gain, besides stranger killing is also increasing. An attempt in the present study has been made to understand the nature and extent of victimization of attempted murder from the Indian Context. The aim of this study is to fill the gap in the literature on victims of attempted murder; however, this study is not to make all encompassing empirical generalizations, but to understand the physical, financial, and psychological impact of victimization. Also the responses of the criminal justice system and the public are analyzed. The results show an extensive pattern of attempted murder victimization, though a sweeping generalization is not made due to certain limitations.

Report from the Middletown Study: The Gradual Progress of Equality in Middletown: A Tocquevillean Theme Re-examined

“The gradual progress of equality,” wrote Tocqueville in his introduction to the first edition of Democracy in America, “is something fated. The main features of this progress are the following: it is universal and permanent; it is daily passing beyond human control, and every event and every man help it along.” That intentionally sweeping generalization has not been disproven by the events of the ensuing century and a half, and the gradual progress of equality continues to be observable in every modern society. Indeed, we are so much further along in that progress that it is now reasonable to inquire about the end-condition toward which it leads us. Will it be a condition of absolute equality or something quite different?

Jacobo De Villaurrutia and the Audiencia of Guatemala, 1794-1804

Scholars are presently re-examining the status of creoles in Spanish colonial administration at the end of the eighteenth century. All historians accept that the Crown discriminated against Americans but the degree and effect of that prejudice is the subject of much current research. Most have rejected Bolívar's sweeping generalization that Spain excluded Americans from all responsible positions, but few agree on the extent of creole participation. Recent studies suggest that creoles held more high positions than had been suspected. These studies further suggest that a new interpretation of the effect of creoles on administration and the independence movement is overdue. The road to this synthesis must be paved with case studies of individuals.

'Frailty, Thy Name is Woman' - How Frail are Women in the World of Shakespeare?

This paper attempts to understand a remarkable point whether we can argue, quoting Hamlet's remark ‘frailty, thy name is woman', that Shakespeare is a misogynist. With that end in view it analyses the situations which lead Hamlet to hold a special kind of prejudice against women. Hence, it examines the justification of his misogynistic remarks in the play. Here the chief concern is whether it is Shakespeare's viewpoint or the view of his character Hamlet; and whether it is deep-rooted, well-thought one or momentary one. Some women characters in several other plays of Shakespeare have been studied, in an endeavor to compare their roles, and to see whether they all show weakness, or some of them surpass the male characters around them in their respective plays. The focus has always been simply on the point whether women are generally frail in the world of Shakespeare. The paper concludes that Hamlet's view does not represent the general view of women in Shakespearean literature; rather it is a sweeping generalization of the misogyny of a young man who has, somehow, been betrayed by women in his life. doi: 10.3329/iiucs.v3i0.2630 IIUC STUDIES Vol. - 3, December 2006 (p 31-44)

Perceived Similarity to Parents as Related to Perceived Similarity to other Adults

109 male college juniors were administered the Role Construct Repertory Test to investigate whether measures of perceived similarity to one's parents are equivalent to perceived similarity to adults in general. The former tended to be consistent with the measures of perceived similarity to some “other adults” and inconsistent with measures of perceived similarity to other “other adults.” Thus, perceived similarity to parents may generalize to other adults because of common characteristics other than adultness between parents and other adults. A sweeping generalization that measures of perceived similarity to parents are equivalent to perceived similarity to adults in general is not warranted.

International Mathematical Education: Mathematics Education in Kenya

Educators in a developing country who are interested in improving their methods and curricula must, of necessity, build upon the work that has been done in other parts of the world. At the same time it is important that they revise and adapt foreign material to their own needs and culture. The present article describes progress in mathematics education in Kenya, which is one of the more developed countries of East Africa. Many of the problems of Kenya are problems of all East Africa, but mathematics teachers need hardly be warned about the danger of making unwarranted generalizations. Contrary to the impression held by some people in the United States, Africa contains a diversity of people with very different cultures and problems about which sweeping generalization is impossible. The reader is also warned that the following remarks are the impressions of an American in the country on a two-year contract, not those of a native Kenyan. This may have resulted in some biases—but these, I hope, are few.